SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Evaluate.
1) ∫ (3x8 - 7x3 + 7) dx Find the integral.
x6
2) ∫ + dx 6x x dx
3) ∫
2 5 (7x + 3) 4) ∫ 16p2e(4p3) dp 1 Solve the problem.
2 5) The rate of expenditure of a particular machine is given by M'(x) = 6x x + 5, where x is time
measured in years. Maintenance costs through the second year are $52. Find the total
maintenance function.
Evaluate the integral.
3
6) ∫ (2x3 - 8x-2) dx Two decimal places.
1 -1
7) ∫ 5x -4 dx Express the answer as a fraction. -2 Evaluate the definite integral.
3x
8) ∫ 2 3 dx Four decimal places. 0 (3x + 3) Use the definite integral to find the area between the x-axis and the graph of f(x) over the indicated interval.
Write the answer as a fraction.
9) 2 f(x) = 2x - x ; [0, 2] 2 3
10) f(x) = ; [1, 3] x3 Find the area of the shaded region.
11) 12) Hint: solve
x- 3 = 0 to find the point needed. Solve the problem.
13)
A certain company has found that its expenditure rate per day (in hundreds of dollars) on a
certain type of job is given by E'(x) = 2x + 4, where x is the number of days since the start of the
job. Find the expenditure if the job takes 6 days. 3 Find the area bounded by the given curves.
3 14)
y = x , y = 4x
Solve the problem.
2 15) Find the consumer's surplus if the demand function for an item is given by D(x) = 30 - x ,
assuming supply and demand are in equilibrium at x = 4. Find the general solution of the differential equation.
dy
16) 2 - 4x
= 24x dx Find the particular solution of the differential equation.
dy
1 17) 2 - 4x + 20; y = 20 when x =
= 6x dx 4

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